Question 3. Let a € (0,1) and define f : T→R by 1 f(x) = sin(nx) na n=1 for all r E (-T, 7]. Prove that f converges for all x E T. (Hint: For r + 0, show E-1 sin(kx)< TanET: Then use Question 3 from the Midterm.) =D1

Q: cos x dx 1 - cos? x d)

A: We have to find the antiderivative if the given part d.

Q: Determine whether the series converges, and if so, find its sum. E-1(-1)k-1 6k-1

A: topic -  series convergence and divergence 

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A: The given series ∑n=1∞nn4+1

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A: topic -  trigonometric function 

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A:

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A: Given that        ∫05e-px dx 

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A: Answer: TRUE

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A: This question can be solved by applying the equation of continuity and integration.

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A: Question- Write an equation for a rational function with:   Vertical asymptotes at x = 1 and x = 3  ...

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A:

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A: This is a problem of differentiation. Based on the general formula of derivative we will calculate t...

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A: Topic = Integration

Q: 3. Use the Comparison Test to determine if the series 5n – cos 2n - n3 + n2 + 1 n=1

A: Given series ∑n=1∞5n-cos2nn3+n2+1 now we use the limit - comparison test

Q: $ Solve and convert to rectangular form. ti sin sin )

A: Since the student has posted multiple questions and does not mention any specific question, so we ar...

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A:

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A: Given function is A = A০ × e^(-0.44t) From given data Ao = 650000$ A=650000*20/100

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A:

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Q: Write an equation for the function graphed below -7 -6

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Q: 3. Use the Comparison Test to determine if the series 5n — сos 2n n³ + n² + 1 n=1 Converges or diver...

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Q: 10. x= cost; y = sin't

A:

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Q: Find the absolute maximum and minimum values of the function on the given set R. (x,y)=(x-2)'+y'; R-...

A:

Q: Let f(x) = 24 /x - 4x. a. Find all points on the graph off at which the tangent line is horizontal. ...

A:

Q: 4. Starting from the same point, Royden starts walking eastward at 0.5 m/s while Nilo starts running...

A: Draw a schematic diagram of given question.

Q: 1. Consider the curve of the function f (x) = 2x² a. Find an expression for the slope of the curve a...

A:

Q: 1dx

A:

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A: Given: f(x)=2x

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A: The graph of y=T(x) is the line tangent to the graph of f at x=4

Q: dx

A: Topic = Integration

Q: x' - x' – 3x – 2 dx x* - x' + 4x? - 4x

A: We will solve the integration using partial fraction. 

Q: dx

A:

Q: 5. The management of Porter Airlines finds that its monthly marginal revenue can be approximated by ...

A: Find your answer below 

Q: Number 62 please

A: 62.] Concept:- For an alternating series let the sum of partial sum is sn then sn - sn-1 for n&gt;= ...

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A:

Q: +oo 2" Use an appropriate test to determine if the series converges or diverges. n+en n=1

A: We will use Ratio Test for the given series.

Q: Q2) For the following problems, find the directional derivative of the given function at the given p...

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Q: 3 sin (x) 4- V1-x2

A: Since you have asked multiple question, we will solve the first question for you. If you want any sp...

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A:

Q: S (1 – cot x) dx b)

A:

Q: 3. Find the arc length of y = 3x3/2 on the interval 1<x< 3 %3D

A:

Q: +00 e-*dx

A: Topic = Integration

Q: Sketch the level curves of the function f(x, y) = y – 3x² for c = 2. 8+ 5- 4 2 -6 -5 -4 -3 -2 -1 4 -...

A: Explanation of the answer is as follows

Q: Use implicit differentiation to find y' for the equation below and then evaluate y' at the indicated...

A:

Q: 2. Use the Integral Test to determine if the series 1 (n+ 2)/4 n=1 converges or diverges.

A: Given problem:-